Sunday Times Teaser 2825 – Twin Sets

by Victor Bryant

The twins Wunce and Repete each made a list of positive perfect squares. In Wunce’s list each of the digits 0 to 9 was used exactly once, whereas in Repete’s list each of the digits was used at least once. Wunce commented that the sum of his squares equalled their year of birth, and Repete responded by saying that the sum of his squares was less than the square of their age [1].

There are problems with the wording of this teaser beyond that noted above. Repete’s list of squares could be [4, 9, 25, 36, 81, 100, 576] with a sum of 831. But we can add 1’s, 4’s or a 9 without exceeding the 841 sum of squares limit set by age of 29. Even if we assume that the lists don’t contain duplicates, we can still add a one to Repete’s set of squares so we don’t know whether his sum is 831 or 832.